Dario Iacoponi, 15, apparently shot himself with his father's gun, which was licensed, at the family home in Ealing, west London, on Tuesday.
Staff and pupils at the Fulham school, attended by Tony Blair's sons Euan, 14, and Nicky, 12, were said to have been shocked at Dario's apparent suicide. He is understood to have been a talented, happy and popular boy with no history of depression.
Reports of a suicide note having been found at the scene were denied by one staff member, although a diary is understood to have been passed to police. Officers are not treating the death as suspicious.
Dario, an only child, was discovered in an upstairs room by a 20-year- old female lodger. His parents were away at the time.
A Scotland Yard spokesman said he had sustained serious head injuries, and added: "A shotgun was found next to the body. The victim's parents were not at the address at the time.
"A post-mortem examination held at Ealing mortuary on November 4 established the cause of death as a gunshot wound to the head."
An inquest has been opened and adjourned.
Earlier this week, another inquest heard how, in an unrelated incident, a choirboy was driven to hang himself by school bullies who burnt him with cigarettes, attacked him,and branded him homosexual. Darren Steele, 15, was found hanging from a cord tied to a window in his bedroom at his home in Burton upon Trent, Staffordshire.Reuse content